It was "an operation of rare difficulty" that grew more complex with the discovery of the American and South Korean hostages being held with the French citizens, Parly said.
Mr Lassimouillas said: "We would like to thank the French authorities and those of Burkina Faso for participating in our liberation, so that we are now very far from all this hell we have been through".
In a statement Friday, Macron expressed condolences over the deaths of the two Marine commandos participating in France's Barkhane Operation, which has been working to root out terrorists roaming the Sahel region.
In that message, Macron also identified the rescued hostages as French tourists Patrick Picque and Laurent Lassimouillas - who were abducted May 1 in Benin.
The badly disfigured body of their guide was found shortly after they disappeared, as well as their abandoned four-wheel Toyota truck. But details about how the Korean woman was taken hostage are not known.
French hostage Laurent Lassimouillas paid tribute to the French soldiers killed during the operation in a short statement, saying, "All our thoughts go to the families of the soldiers and the soldiers who lost their lives to free us from this hell, we wanted to offer our condolences right away".
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It was still unclear how the American and South Korean ended up as hostages.
Four of the six kidnappers were killed, but two French soldiers also died in the raid. One official said that the USA support was in the form of overhead intelligence, surveillance and reconnaissance.
France's army chief Francois Lecointre told reporters the rescue operation came on the back of a reconnaissance mission that returned vital information on the gang of six hostage-takers.
The three will fly to a military airport outside the French capital on Saturday evening where they will be welcomed by President Emmanuel Macron.
"The greatest precautions must be taken in these regions to avoid these types of kidnappings, and avoid the sacrifices required by our soldiers", he said.
France has 4,500 troops in a military force in the Sahel aimed at helping local governments fight Islamic extremists.